Quantum private comparison of arbitrary single qubit states based on swap test

Abstract

In this paper, by using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any participants. In the process of comparison, TP cannot get two participants' private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participant attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, and it can compare two participants' qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.

Efficient Quantum Private Comparison without Sharing a Key

“…The one used in the proposed protocol is |GHZ 1 , in which the ∆ has a value of 0 and q 2 = q 3 = 0. |GHZ 1 is a GHZ state, which is shown as Equation (5).…”

“…QKD technology primarily relies on the fundamental principles of quantum mechanics to ensure that users generate secure and dependable keys during the communication progress [3,4]. Moreover, the goal of quantum private comparison is to enable both parties to compare their secret data without revealing any information about the data to each other or any potential eavesdropper [5][6][7]. QPC has potential applications in a variety of fields, including secure online voting, financial transactions, and data sharing between government agencies.…”

Single-photon-based quantum secure protocol for the socialist millionaires’ problem

“…This protocol requires a two-particle quantum walk state and a quantum walk operator, and it can improve efficiency by allowing private inputs to be compared all at once rather than bit by bit. In order to compare the relationship of arbitrary singlequbit states, Huang et al [31] constructed a QPC protocol by utilizing the special property of rotation encryption and swap test.…”

New Quantum Private Comparison Using Four-Particle Cluster State

“…In this protocol, secrets are divided into multiple groups, which improves efficiency by eliminating the need to compare all groups of information. Since then, different QPC protocols have been continuously proposed, aiming to determine the relationship between private and these studies mainly utilize various quantum states, including single photons [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ], Bell states [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 ], entangled states [ 34 , 35 , 36 , 37 , 38 , 39 ], cluster states [ 40 , 41 , 42 , 43 , 44 , 45 ] and d-level quantum states [ 46 , 47 , 48 , 49 ] as quantum resources. They also employ different quantum technologies, such as entanglement swapping and unitary operations, as well as determine whether to distribute keys for sharing secret keys to accomplish the comparison.…”